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Question
If the length of a median of an equilateral triangle is x cm, then its area is
Options
x2
- \[\frac{\sqrt{3}}{2} x^2\]
- \[\frac{x^2}{\sqrt{3}}\]
- \[\frac{x^2}{2}\]
Solution
We are given the length of median of an equilateral triangle by which we can calculate its side. We are asked to find area of triangle in terms of x
Altitude of an equilateral triangle say L, having equal sides of a cm is given by, where, L = x cm
`x = sqrt(3)/2 a`
`a = 2/sqrt(3) x cm `
Area of an equilateral triangle, say A1 having each side a cm is given by
`A_1 = sqrt(3)/4 a^2`
Since `a = 2/sqrt(3) x cm `.So
`A_1 = sqrt (3)/4 (2/sqrt(3) x )^2`
`A_1 = sqrt(3)/4 xx (4x^2)/3`
`A_1 = x^2/sqrt(3)`
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